The Collaborative International Dictionary of English v.0.48:

irresponsibleness \irresponsibleness\ n.
   the habitual failure to behave in a responsible manner;
   irresponsibility.

   Syn: irresponsibility.
        [WordNet 1.5]

WordNet (r) 3.0 (2006):

irresponsibleness
    n 1: a form of untrustworthiness; the trait of lacking a sense
         of responsibility and not feeling accountable for your
         actions [syn: irresponsibility, irresponsibleness]
         [ant: responsibility, responsibleness]